FIG. 4 shows a conventional type of constant-voltage circuit (reference voltage source circuit) using the band-gap reference voltage of the bipolar transistor.
The constant-current circuit shown in FIG. 4 has battery 21, current source circuit 23, and band-gap reference circuit 25.
As shown in the figure, band-gap reference circuit 25 is made of the following elements connected to each other: resistor element R.sub.21, npn-type bipolar transistor Q.sub.21, resistor element R.sub.22, npn-type bipolar transistor Q.sub.22, resistor element R.sub.23, and npn-type bipolar transistor Q.sub.23.
As the reference voltage V.sub.ref in band-gap reference circuit 25 is determined by the energy band-gap voltage V.sub.BG (1.205 V) of silicon-extrapolated to Kelvin temperature 0.degree. K., reference voltage V.sub.ref is called the band-gap reference.
Current source circuit 23 acts as the current source of band-gap reference circuit 25, and a constant current I.sub.23 is fed to band-gap reference circuit 25.
For example, transistor Q.sub.22 operates with a current density about 10 times that of transistor Q.sub.22, and a difference of base-emitter voltage .DELTA.V.sub.BE between transistor Q.sub.21 and transistor Q.sub.22 is generated between the terminals of resistor element R.sub.23.
When the current gain of the transistor is high, voltage V.sub.R22 between the terminals of resistor element R.sub.22 as represented by the following formula is generated: EQU V.sub.R.sbsb.22 .DELTA.V.sub.BE (RV.sub.23 /RV.sub.22) (1)
where,
RV.sub.22 is the resistance of resistor element R.sub.22, and PA1 RV.sub.23 is the resistance of resistor element R.sub.23. PA1 V.sub.BE22 represents the base-emitter voltage of Q.sub.22. PA1 T is the operation temperature (Kelvin temperature K) of the bipolar transistor; PA1 T.sub.0 represents absolute zero (0.degree. K.); PA1 V.sub.G0 represents the energy band-gap voltage at absolute zero; and PA1 V.sub.BE0 represents base-emitter voltage at T.sub.0 with a collector current of I.sub.C0 at T.sub.0. PA1 k is Boltzman constant, and PA1 q is the charge of electron.
In this band-gap reference circuit 25, band-gap reference voltage V.sub.BG (reference voltage V.sub.ref) can be represented as follows: EQU V.sub.BG =V.sub.ref =V.sub.BE22 +(RV.sub.23 /RV.sub.22).multidot..DELTA.V.sub.BE ( 2)
where,
This energy band-gap voltage V.sub.BG is reference voltage V.sub.ref, and it is fed as output voltage V.sub.OUT of the constant-voltage circuit to the load.
Transistor Q.sub.23 forms the gain section that stabilizes the aforementioned energy band-gap voltage V.sub.BG.
The temperature compensation for band-gap reference circuit 25 is performed as follows:
The base-emitter voltage V.sub.BE of the bipolar transistor can be represented as follows: EQU V.sub.BE .apprxeq.V.sub.G0 (1-T/T.sub.0)+V.sub.BE0 (T/T.sub.0) (3)
where,
When the current densities of transistors Q.sub.21 and Q.sub.22 are J.sub.1 and J.sub.2, respectively, the difference voltage .DELTA.V.sub.BE of the base-emitter voltage between these two transistors becomes: EQU .DELTA.V.sub.BE =(kT/q) ln (J.sub.1 /J.sub.2) (4)
where,
From formulas 2-4, reference voltage V.sub.ref is represented by the following formula: ##EQU1##
When reference voltage V.sub.ref is partially differentiated with respect to the absolute temperature T, one has: +(RV.sub.23 /RV.sub.22) (kT.sub.0 /q) ln (J.sub.1 /J.sub.2) (6)
The temperature compensation condition for the independence of reference temperature V.sub.ref on the temperature is EQU .differential.V.sub.ref /.differential.T=0
and one has: EQU V.sub.G0 =V.sub.BE0 +(RV.sub.23 /RV.sub.22) (kT.sub.0 /q) ln (J.sub.1 /J.sub.2) (7)
When this band-gap [voltage] V.sub.G0 is substituted into formula 5, one has: EQU V.sub.ref =V.sub.BE22 +(RV.sub.23 /RV.sub.22) (kT.sub.0 /q) ln (J.sub.1 /J.sub.2) (8)
As reference voltage V.sub.ref in this formula does not contain operation temperature T, there is no dependence on the temperature.
As can be seen from formula (4), (kT.sub.0 /q)ln(J.sub.1 /J.sub.2) is .DELTA.V.sub.BE0 at temperature T.sub.0 ; hence, reference voltage V.sub.ref can be represented by the following formula: EQU V.sub.ref =V.sub.BE22 +(RV.sub.23 /RV.sub.22) .DELTA.V.sub.BE0 ( 9)
As base-emitter voltage V.sub.BE22 of transistor Q.sub.22 has a negative temperature coefficient, while resistor element R.sub.23 has a positive temperature coefficient, difference voltage .DELTA.V.sub.BE of the base-emitter voltage between the two transistors, that is, voltage between terminals V.sub.R23, has a positive temperature coefficient.
As can be seen from the aforementioned analysis, by setting appropriately the ratio of resistance of the voltage dividing resistor elements (RV.sub.22 /RV.sub.23), the base-emitter voltage V.sub.BE22 of transistor Q.sub.22 and (RV.sub.22 /RV.sub.23).multidot..DELTA.V.sub.BE (or, (RV.sub.22 /RV.sub.23).multidot.V.sub.R23) cancel each other, and the temperature coefficient of energy band-gap voltage V.sub.BG approaches "0".
The base-emitter voltage V.sub.BE22 of bipolar transistor Q.sub.22 is about 0.6-0.7 V; when (RV.sub.23 /RV.sub.22).DELTA.V.sub.BE0 in the case of temperature compensation is taken into consideration, the band-gap reference voltage V.sub.BG of silicon is usually about 1.2 V.
Consequently, battery 21 used for operation of band-gap reference circuit 25 should be a battery with an output voltage of 1.2 V or higher. Usually, a battery with an output voltage of about 1.5 V is used.
Recently, for electronic devices, there is a tendency toward reducing the size, the voltage, and the power consumption. Accordingly, there is a demand on using a small-sized low-voltage battery to drive band-gap reference circuit 25.
For example, there is a high demand on using only a single battery with a small size and a voltage lower than 1 V, such as a nickel-cadmium battery of about 0.9 V to drive a constant-voltage circuit which generates a temperature-compensated reference voltage lower than 1 V.
However, the constant-voltage circuit using the conventional band-gap reference circuit 25 as shown in FIG. 4 cannot meet the aforementioned demand.